brake trouble

Blowing air thru is not a problem. I do that all the time, plus ethanol then dry. But, I have each individual tube open on both ends. I did on several cars before changing to silicone fluid (for no more rust).

I'll 2nd that the "imbalance warning switch" cannot block flow thru the "distribution block" in which it sits. If its piston is stuck on one side (common in rusty systems), its terminal will short to gnd which should light your dash warning lamp. BTW, there is a procedure to re-center the piston in a factory manual, once you get all the air out.

I have never tried gravity bleeding, but many here says it works for them. Try the old method: helper at the pedal with call-response to other at each bleeder. My wife is trained.